The CADE ATP System Competition (CASC) is the annual evaluation of fully automatic, classical logic Automated Theorem Proving (ATP) systems. CASC-28 was the twenty-sixth competition in the CASC series. Twenty-two ATP systems competed in the various competition divisions. This paper presents an outline of the competition design and a commentated summary of the results.
P.B.Andrews, M.Bishop, S.Issar, D.Nesmith, F.Pfenning and H.Xi, TPS: A theorem-proving system for classical type theory, Journal of Automated Reasoning16(3) (1996), 321–353. doi:10.1007/BF00252180.
2.
P.B.Andrews and C.E.Brown, TPS: A hybrid automatic-interactive system for developing proofs, Journal of Applied Logic4(4) (2006), 367–395. doi:10.1016/j.jal.2005.10.002.
3.
L.Bachmair and N.Dershowitz, Critical pair criteria for completion, Journal of Symbolic Computation6(1) (1988), 1–18. doi:10.1016/S0747-7171(88)80018-X.
4.
A.Bentkamp, J.Blanchette, S.Cruanes and U.Waldmann, Superposition for lambda-free higher-order logic, Logical Methods in Computer Science17(2) (2021), Online.
5.
A.Bentkamp, J.Blanchette, S.Tourret and P.Vukmirović, Superposition for full higher-order logic, in: Proceedings of the 28th International Conference on Automated Deduction, A.Platzer and G.Sutcliffe, eds, Lecture Notes in Computer Science, Springer-Verlag, 2021, pp. 396–412.
6.
J.Blanchette, P.Fontaine, S.Schulz and U.Waldmann, Towards strong higher-order automation for fast interactive verification, in: Proceedings of the 1st International Workshop on Automated Reasoning: Challenges, Applications, Directions, Exemplary Achievements, G.Reger and D.Trayfel, eds, EPiC Series in Computing, EasyChair Publications, 2017, pp. 16–23.
7.
C.E.Brown, Satallax: An automated higher-order prover (system description), in: Proceedings of the 6th International Joint Conference on Automated Reasoning, B.Gramlich, D.Miller and U.Sattler, eds, Lecture Notes in Artificial Intelligence, 2012, pp. 111–117.
8.
K.Claessen and N.Smallbone, Efficient encodings of first-order horn formulas in equational logic, in: Proceedings of the 9th International Joint Conference on Automated Reasoning, D.Galmiche, S.Schulz and R.Sebastiani, eds, Lecture Notes in Computer Science, 2018, pp. 388–404.
9.
L.de Moura and N.Bjørner, Z3: An efficient SMT solver, in: Proceedings of the 14th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, C.Ramakrishnan and J.Rehof, eds, Lecture Notes in Artificial Intelligence, Springer-Verlag, 2008, pp. 337–340.
10.
A.Duarte and K.Korovin, Implementing superposition in iProver, in: Proceedings of the 10th International Joint Conference on Automated Reasoning, N.Peltier and V.Sofronie-Stokkermans, eds, Lecture Notes in Artificial Intelligence, 2020, pp. 388–397.
11.
A.Duarte and K.Korovin, AC simplifications and closure redundancies in the superposition calculus, in: Proceedings of the 30th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, A.Das and S.Negri, eds, Lecture Notes in Artificial Intelligence, Springer-Verlag, 2021, pp. 200–217. doi:10.1007/978-3-030-86059-2_12.
12.
N.Eén and N.Sörensson, An extensible SAT-solver, in: Proceedings of the 6th International Conference on Theory and Applications of Satisfiability Testing, E.Giunchiglia and A.Tacchella, eds, Lecture Notes in Computer Science, Springer-Verlag, 2004, pp. 502–518. doi:10.1007/978-3-540-24605-3_37.
13.
J.Hernandez and K.Korovin, An abstraction-refinement framework for reasoning with large theories, in: Proceedings of the 9th International Joint Conference on Automated Reasoning, D.Galmiche, S.Schulz and R.Sebastiani, eds, Lecture Notes in Computer Science, 2018, pp. 663–679.
14.
T.Hillenbrand, A.Jaeger and B.Löchner, Waldmeister – improvements in performance and ease of use, in: Proceedings of the 16th International Conference on Automated Deduction, H.Ganzinger, ed., Lecture Notes in Artificial Intelligence, Springer-Verlag, 1999, pp. 232–236. doi:10.1007/3-540-48660-7_20.
15.
E.Holden and K.Korovin, SMAC and XGBoost your theorem prover, in: Proceedings of the 4th Conference on Artificial Intelligence and Theorem Proving, T.Hales, C.Kaliszyk, R.Kumar, S.Schulz and J.Urban, eds, 2019, pp. 93–95.
16.
E.Holden and K.Korovin, Heterogeneous heuristic optimisation and scheduling for first-order theorem proving, in: Proceedings of the 14th International Conference on Intelligent Computer Mathematics, F.Kamareddine and C.Sacerdoti, eds, Lecture Notes in Computer Science, Springer-Verlag, 2021, pp. 107–123. doi:10.1007/978-3-030-81097-9_8.
17.
K.Korovin, iProver – an instantiation-based theorem prover for first-order logic (system description), in: Proceedings of the 4th International Joint Conference on Automated Reasoning, P.Baumgartner, A.Armando and G.Dowek, eds, Lecture Notes in Artificial Intelligence, 2008, pp. 292–298.
18.
K.Korovin, Inst-Gen – a modular approach to instantiation-based automated reasoning, in: Programming Logics, Essays in Memory of Harald Ganzinger, A.Voronkov and C.Weidenbach, eds, Lecture Notes in Computer Science, Springer-Verlag, 2013, pp. 239–270. doi:10.1007/978-3-642-37651-1_10.
19.
E.Kotelnikov, L.Kovacs, M.Suda and A.Voronkov, A clausal normal form translation for FOOL, in: Proceedings of the 2nd Global Conference on Artificial Intelligence, C.Benzmüller, G.Sutcliffe and R.Rojas, eds, EPiC Series in Computing, EasyChair Publications, 2016, pp. 53–71.
20.
L.Kovacs and A.Voronkov, First-order theorem proving and vampire, in: Proceedings of the 25th International Conference on Computer Aided Verification, N.Sharygina and H.Veith, eds, Lecture Notes in Artificial Intelligence, Springer-Verlag, 2013, pp. 1–35.
21.
U.Martin and T.Nipkow, Ordered rewriting and confluence, in: Proceedings of the 10th International Conference on Automated Deduction, M.E.Stickel, ed., Lecture Notes in Artificial Intelligence, Springer-Verlag, 1990, pp. 366–380. doi:10.1007/3-540-52885-7_100.
22.
L.Paulson and J.Blanchette, Three years of experience with sledgehammer, a practical link between automatic and interactive theorem provers, in: Proceedings of the 8th International Workshop on the Implementation of Logics, G.Sutcliffe, E.Ternovska and S.Schulz, eds, EPiC Series in Computing, EasyChair Publications, 2010, pp. 1–11.
23.
A.Schlichtkrull, J.Blanchette and D.Traytel, A verified prover based on ordered resolution, in: Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs, A.Mahboubi and M.Myreen, eds, ACM Press, 2019, pp. 152–165. doi:10.1145/3293880.3294100.
24.
A.Schlichtkrull, J.Blanchette, D.Traytel and U.Waldmann, Formalizing Bachmair and Ganzinger’s ordered resolution prover, Journal of Automated Reasoning64(7) (2020), 1169–1195. doi:10.1007/s10817-020-09561-0.
25.
S.Schulz, Simple and efficient clause subsumption with feature vector indexing, in: Automated Reasoning and Mathematics: Essays in Memory of William, W.McCune, M.P.Bonacina and M.Stickel, eds, Lecture Notes in Artificial Intelligence, Springer-Verlag, 2013, pp. 45–67. doi:10.1007/978-3-642-36675-8_3.
26.
S.Schulz, S.Cruanes and P.Vukmirovic, Faster, higher, stronger: E 2.3, in: Proceedings of the 27th International Conference on Automated Deduction, P.Fontaine, ed., Lecture Notes in Computer Science, Springer-Verlag, 2019, pp. 495–507.
27.
N.Smallbone, Twee: An equational theorem prover (system description), in: Proceedings of the 28th International Conference on Automated Deduction, A.Platzer and G.Sutcliffe, eds, Lecture Notes in Computer Science, Springer-Verlag, 2021, pp. 602–613.
28.
A.Stump, G.Sutcliffe and C.Tinelli, StarExec: A cross-community infrastructure for logic solving, in: Proceedings of the 7th International Joint Conference on Automated Reasoning, S.Demri, D.Kapur and C.Weidenbach, eds, Lecture Notes in Artificial Intelligence, 2014, pp. 367–373.
29.
G.Sutcliffe, The CADE-16 ATP system competition, Journal of Automated Reasoning24(3) (2000), 371–396. doi:10.1023/A:1006393501098.
30.
G.Sutcliffe, The 7th IJCAR automated theorem proving system competition – CASC-J7, AI Communications28(4) (2015), 683–692. doi:10.3233/AIC-150668.
31.
G.Sutcliffe, The CADE ATP system competition – CASC, AI Magazine37(2) (2016), 99–101. doi:10.1609/aimag.v37i2.2620.
32.
G.Sutcliffe, The TPTP problem library and associated infrastructure. From CNF to TH0, TPTP v6.4.0, Journal of Automated Reasoning59(4) (2017), 483–502. doi:10.1007/s10817-017-9407-7.
33.
G.Sutcliffe, The CADE-27 automated theorem proving system competition – CASC-27, AI Communications32(5–6) (2020), 373–389. doi:10.3233/AIC-190627.
34.
G.Sutcliffe, The 10th IJCAR automated theorem proving system competition – CASC-J10, AI Communications34(2) (2021), 164–177. doi:10.3233/AIC-201566.
35.
G.Sutcliffe, Proceedings of the CADE-28 ATP System Competition, Online, 2021, http://www.tptp.org/CASC/28/Proceedings.pdf.
36.
G.Sutcliffe and C.B.Suttner, Evaluating general purpose automated theorem proving systems, Artificial Intelligence131(1–2) (2001), 39–54. doi:10.1016/S0004-3702(01)00113-8.
37.
G.Sutcliffe, J.Zimmer and S.Schulz, TSTP data-exchange formats for automated theorem proving tools, in: Distributed Constraint Problem Solving and Reasoning in Multi-Agent Systems, W.Zhang and V.Sorge, eds, Frontiers in Artificial Intelligence and Applications, IOS Press, 2004, pp. 201–215.
38.
P.Vukmirović, A.Bentkamp, J.Blanchette, S.Cruanes, V.Nummelin and S.Tourret, Making higher-order superposition work, in: Proceedings of the 28th International Conference on Automated Deduction, A.Platzer and G.Sutcliffe, eds, Lecture Notes in Computer Science, Springer-Verlag, 2021, pp. 415–432.
39.
P.Vukmirovic, J.Blanchette, S.Cruanes and S.Schulz, Extending a brainiac prover to lambda-free higher-order logic, in: Proceedings of the 25th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, T.Vojnar and L.Zhang, eds, Lecture Notes in Computer Science, Springer-Verlag, 2019, pp. 192–210.